Tonight when I started up the PC, the ethernet is working. Yea! One mystery solved, though I don't know what did it.
Regarding the output of lspci, for the wireless, it is Broadcom Corporation BCM4306 802.11b/G Wireless LAN controller (rev 03).
About wicd, I am trying to install that and I am getting an Error that says:
E: Write error 0 write (28L No space left on device)
E: IO Error saving source cache
E: THe package lists or status file could not be parsed or opened.
Any thoughts?